A Molecular Model of the Elastic Behavior of Polymethylene Chains

In this paper, the elastic behavior of a polymethylene (PM) chain is investigated by using a realistic rotational‐isomeric‐state (RIS) model. In our calculation, the non‐local interactions between pairs of segments in a polymethylene chain are also considered, and the Lennard‐Jones (L‐J) potential function is adopted. Chain dimensions and thermodynamics statistical properties of PM chains with various elongation ratios λ are calculated. We find, that the elastic force increases slowly with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant, especially for large λ. Our calculations may provide some insight into the macroscopic phenomena of rubber elasticity.     

Monte Carlo Studies on the Deformation Behavior of Entangled Polymer Chains

In this work we present a continuous three‐dimensional bond‐fluctuation model (CBFM) in combination with the method of confined self‐avoiding walks (CSAW). This method enables us to analyse both the compression and the stretching regime of the deformation process of two entangled polymer chains. We studied the deformation behavior in respect to the number of entanglements, the distance of the end monomers on the confining surfaces and the orientation of the entanglements to the deformation axis. Our analysis of the behavior of the force and the structural properties of the systems during the deformation process leads us to the assumption that the entanglements act as one topological crosslink with variable strength.     

聚亚甲基链在弹性形变时的链段取向研究

高聚物的弹性形变是一个重要而普遍的现象 .在弹性形变过程中链段取向问题的研究是高聚物弹态形变中一个十分重要的内容 [1～ 6 ] ,这主要是 :一方面 ,在弹性形变过程中的链段取向可用核磁共振和红外二向色性实验方法直接测定 [2～ 4 ] ,另一方面 ,它又与高聚物在弹性形变过程中统计性质密切相关[1,5,6 ] ,因此对链段取向的研究可加深对弹性形变过程的了解 .最近 Taylor等[7] 用 Monte Carlo方法研究了聚亚甲基链的链段取向问题 ,但未研究高聚物在弹性形变过程中的内能变化 [8] ,也未考虑远程相互作用和较短的高分子链情况 ,这通常与理想…     

Structure of Adsorbed Polymer Chains: A Monte Carlo Study

The structure of adsorbed polymer chains was studied using simplified lattice models. The model chains were adsorbed on an impenetrable surface with an attractive potential. The dynamic Monte Carlo simulations based in the Metropolis scheme were carried out using these models. The influence of the internal chain architecture (linear, star‐branched and ring chains) and the degree of adsorption on the chain's structure was studied. It was shown that for weakly adsorbed chain regime the ring polymers which exhibit an almost twice as high degree of adsorption compared to linear and star chains have a higher number of adsorbed parts of chain (trains). But the length of such train remains almost the same for all types of a polymer chain. Star‐branched chains exhibit a slightly different change in number and the mean length of trains, loops and tails with the temperature and the chain total length compared to two other types of chain.     

聚亚甲基链的温度系数

本文采用旋转异构态模型,考虑排斥体积效应,用 Monte Carlo模拟方法计算了聚亚甲基高分子链的温度系数dln/dT。考虑排斥体积的聚亚甲基链的温度系数大于无扰聚亚甲基链的温度系数,并更接近实验值。     

Elastic Behavior of Polymer Chains

The elastic behavior of the polymer chain was investigated in a three-dimensional off-lattice model. We sample more than 109 conformations of each kind of polymer chain by using a Monte Carlo algorithm, then analyze them with the non-Gaussian theory of rubberlike elasticity, and end with a statistical study. Through observing the effect of the chain flexibility and the stretching ratio on the mean-square end-to-end distance, the average energy, the average Helmholtz free energy, the elastic force, the contribution of energy to the elastic force, and the entropy contribution to elastic force of the polymer chain, we find that a rigid polymer chain is much easier to stretch than a flexible polymer chain. Also, a rigid polymer chain will become difficult to stretch only at a quite high stretching ratio because of the effect of the entropy contribution. These results of our simulation calculation may explain some of the macroscopic phenomena of polymer and biomacromolecular elasticity.     

拉伸分子动力学方法研究聚乙烯单链的力学行为

采用拉伸分子动力学方法(steered molecular dynamics,SMD)研究一端固定的聚乙烯单链(singlepolyethylene chain)在被拉伸过程中的力学性质.在拉伸过程中发现平均拉力〈f〉受拉伸速度v的影响,当v<0.05 nm/ps时,〈f〉在250 pN附近会出现一个拉力平台.聚乙烯单链各部分的形状因子在拉伸过程中表现出一定的规律性,总是头部和尾部的形状因子〈δh〉、〈tδ〉先增加然后才是中间部分〈δm〉增加.如果按顺序再释放被拉开的聚乙烯单链,就会出现力学回滞现象,这与Kellermayer等的力学回滞曲线实验是一致的.力学回滞曲线面积表示耗散能〈Ed〉,与速度v满足方程〈Ed〉=a+b×e-cv,而且在v<0.005 nm/ps和v>0.005 nm/ps两个速度区域有不同的特性.〈Ed〉在不同的分子热运动温度区域,也表现出不同的规律性,当温度T>220 K时,〈Ed〉随着温度T的升高而减小,这与Pegoretti等的实验一致,当T<220 K时〈Ed〉随着温度T的升高而增加.     

端点附壁的高分子链形状的Monte Carlo模拟

分别基于简立方格点和四面体格点模型对一端吸附在无限大平面的高分子链（平面接枝高分子链）的形状进行了Ｍｏｎｔｅ Ｃａｒｌｏ模拟,结果表明,接枝高分子链的形状更偏离球形,〈Ｌ＾２１〉：〈Ｌ＾２２〉：〈Ｌ＾２３〉的极限值约为１：２．７５：１２．５,其中〈Ｌ＾２１〉,〈Ｌ＾２２〉和〈Ｌ＾２３〉分别为回转半径张量的本征值Ｌ＾２１,Ｌ＾２２和Ｌ＾２３（Ｌ＾２１〈Ｌ＾２２〈Ｌ＾２３）的统计平均;链长相同时,接枝     

Folding Behavior of Polypeptides. A Monte Carlo Study of Simplified Models

A simple model of polypeptide chains was designed and studied. The chains were constructed on a flexible [310] lattice and consisted of united atoms located at the position of alpha carbons. Each united atom represented amino acid residues of two kinds: hydrophilic and hydrophobic. The sequence of the residues was assumed to be characteristic for α- and β-type of proteins. The force field used consisted of the long-range contact potential between polymer segments, the short range repulsion, and the local potential preferring conformational states characteristic for α-helices and β-strands. The Monte Carlo simulations of this model were carried out using the replica exchange technique coupled with the histogram method. The influence of temperature and the local potential on the size and internal structure of collapsed low temperature chains were studied. Thermodynamics of these systems consisting mainly of α and β secondary structures were determined. The properties of the coil-to-globule transition were presented and compared with other theoretical predictions and simulation results.     

Folding Behavior of Polypeptides. A Monte Carlo Study of Simplified Models

Summary. A simple model of polypeptide chains was designed and studied. The chains were constructed on a flexible [310] lattice and consisted of united atoms located at the position of alpha carbons. Each united atom represented amino acid residues of two kinds: hydrophilic and hydrophobic. The sequence of the residues was assumed to be characteristic for α- and β-type of proteins. The force field used consisted of the long-range contact potential between polymer segments, the short range repulsion, and the local potential preferring conformational states characteristic for α-helices and β-strands. The Monte Carlo simulations of this model were carried out using the replica exchange technique coupled with the histogram method. The influence of temperature and the local potential on the size and internal structure of collapsed low temperature chains were studied. Thermodynamics of these systems consisting mainly of α and β secondary structures were determined. The properties of the coil-to-globule transition were presented and compared with other theoretical predictions and simulation results.     

Adsorption of Semiflexible Chains on Nanostriped Surfaces: Monte Carlo Simulations

Monte Carlo simulations were carried out to investigate the adsorption of semiflexible chains from a semidilute solution to substrates with periodic stripes of width w. The chains are made of fused N = 10 monomers of diameter σ interacting with each other through excluded volume interactions and with the stripes via a square‐well potential of depth ε and width σ. The surface coverage was found to increase upon increasing the chain stiffness and decreases on increasing the width of the stripes. At small w, more flexible chains are adsorbed than stiff chains. Analysis of the radius of gyration for the chains showed that when w < 8σ, the component along the stripe direction is significantly larger than the others. Orientational order parameter reveals that, for small w, chains have preference to align along the stripe direction.

     

Elastic properties of soft sphere crystal from Monte Carlo simulations

Elastic properties of faced centered cubic (fcc) crystals composed of soft spheres, interacting through potentials of the form u(r) ~ r(-n), have been investigated by Monte Carlo (MC) simulations. It is shown that both the softness parameter (n(-1)) and temperature strongly influence the elastic properties of the studied system. The simulations show explicitly that when T > 0 the elastic constants of the hard sphere crystal can be obtained by taking the limit n --> infinity of soft spheres. When T --> 0 for any finite n, the elastic constants of the soft spheres tend to those of the static model. At all temperatures and softness parameters studied here, n, the Poisson's ratio in [110] (perpendicular direction) is negative.     

Monte Carlo模拟研究抗体-抗原复合物生长的标度行为

通过Monte Carlo模拟方法对抗体-抗原复合物在等活性和非等活性条件下生长的标度行为进行了研究. 模拟所用算法的有效性通过在等活性条件下的模拟结果与解析结果之间的一致性得以证明. 在模拟中, 主要考察了抗体-抗原复合物的数量分布函数、重均聚合度以及特征关联长度在临界点附近的标度行为, 给出相应的标度指数, 并以其检验溶胶-凝胶相变的广义标度律. 研究结果表明, 非等活性对抗体-抗原复合物的生长具有显著影响, 可为临床免疫分析提供相应的理论线索.     

高分子链形状与尺寸关联的Monte Carlo模拟

运用MonteCarlo方法对线型高分子链格点模型的构型进行了模拟,研究了构型的尺寸(采用平方末端距R²,平方回转半径S²来表征)和形状(由非球形因子A表征)之间的关联.对任何长度的高分子链,其关联系数CA,R²和CA,S²均为正值,表明高分子链的形状与尺寸之间存在正关联,即尺寸小的构型其非球形因子A一般也小,反之尺寸大的构型其非球形因子A一般也大.关联系数CA,R²和CA,S²均随链长的增大而减小,近似地与链长的倒数(n^-1)成正比.研究还表明,关联系数的极限值(链长n很大时)与格点的类型无关,与链样本产生的方式也无关,但与链是否考虑排斥体积有关,考虑了排斥体积后,关联系数增大.     

Conformation of Chains in Cores of Block Copolymer Micelles with Solubilized Homopolymer: a Monte Carlo Study

A system of compatible self‐avoiding polymer chains solubilized in spherical cores of block copolymer micelles was studied by lattice Monte Carlo simulations. The core is modeled as a spherical cavity on a simple cubic lattice, filled in partially by tethered (core‐forming) chains and partially by free (solubilized) chains. Molecular parameters (e.g., the ratio of the contour length of the model chains to the core radius) correspond to those in real micellar systems. The density (the fraction of lattice sites occupied) is 0.6 which corresponds to swollen micellar cores in real micellar systems. Simulations yield a constant segment density profile in the core. Both the tethered and solubilized chains acquire an ellipsoidal shape. The ellipsoids equivalent to both types of chains are more spherical than those in a melt and strongly oriented. The chains in the core show a Gaussian‐like behavior. Minor deviations from Gaussian behavior for tethered chains are due to surface effects.     

Monitoring Diffusion of Reptating Polymer Chains by a Direct Energy Transfer Method: A Monte Carlo Simulation

A kinetic Monte Carlo method was used to simulate the diffusion of reptating polymer chains across an interface. A time‐resolved fluorescence technique in conjunction with a direct energy transfer method was used to measure the extent of diffusion of dye‐labeled reptating polymer chains. The diffusion of donor‐ and acceptor‐labeled polymer chains between adjacent compartments was randomly generated. The fluorescence decay profiles of donor molecules were simulated at several diffusion steps to produce mixing of the polymer chains. Mixing ratios of donor‐ and acceptor‐labeled polymer chains in compartments were measured at various stages (snapshots) of diffusion. It was observed that for a given molecular weight, the average interpenetration contour length was found to be proportional to the mixing ratio. Monte Carlo analysis showed that the curvilinear diffusion coefficient is inversely proportional to the weight of polymer chains during diffusion.     

表面单层组装多环芳烃荧光行为的Monte Carlo模拟

Recently,a series of sensing films based upon the supra-molecular behavior of aromatic compounds immobilized on substrate surfaces and its dependence to the composition of the medium have been successfully prepared. It is found that the properties and performances of the films depend upon various factors,including the nature of the sensing element,the way of immobilization,the nature of the substrate,and the density of the sensing element immobilized etc. To accelerate and deepen the studies,it was decided to carry out the theoretical simulation of the sensing films based upon the proposed principle. The fluorescence behavior of a functional plate,of which the surface is functionalized by single layer immobilization of aromatic compounds（sensing elements）,is simulated by Monte Carlo simulation method. The effects of the immobilization density of a sensing element,the excitation efficiency,and the association efficiency,P,which is a characteristic parameter of an aromatic compound,between the molecules of the sensing element on the ratio of the excimer emission to the monomer emission of the plate have been systematically examined. But the effects of the length and flexibility of a spacer are neglected,because in this simulation aromatic compounds are immobilized on a plate by the short stiff spacer. It is demonstrated that,for a functionalized plate of a short stiff spacer in a polar solvent（ in this case,the association tendency is strong,and P is close to 1）,aromatic compounds of middle excitation efficiency might be suitable as sensing elements. In addition,the immobilization density of the sensing element should be controlled. A recommended value is about 50%.     

Kinetic Monte Carlo Studies on the Importance of the Reaction Scheme in Segmental Exchange of Copolymer Chains

Kinetic Monte Carlo studies (confirmed by integration of the corresponding differential equations) are used to demonstrate the fundamental differences between the two most often accepted schemes of segmental exchange. Modeling of reshuffling systems, originally composed of homopolymers of various , various mass distributions, and different compositions, is carried out until the equilibrium copolymers are obtained. It is shown that one of the schemes leads always to a random microstructure (Bernoulli statistics) whereas modeling of the other one indicates possibility of formation of all achievable distributions of comonomer units (from multiblock to nearly alternate). The concepts of the degrees of randomness and reshuffling are discussed and new definitions are proposed.

     

聚硅烷链形状的Monte Carlo研究

用ＭｏｎｔｅＣａｒｌｏ方法对θ溶液中考虑二级相互作用的聚硅烷链的形状进行了研究。结果表明聚硅烷链的形状明显偏离球形，它与链长有关，长链极限的比值＜Ｌ２１＞∶＜Ｌ２２＞∶＜Ｌ２３＞约为１∶２．７∶１２．１。还发现聚硅烷链转动惯量的最长主轴与末端距矢量之间夹角的统计平均值＜θ＞的极限值约为２７°。     

Monte Carlo Simulation of Coil-to-Globule Transition of Compact Polymer Chains: Role of Monomer Interacting

Coil-to-globule transitions are fundamental problems existing in polymer science for several decades; however, some features are still unclear, such as the effect of chain monomer interaction. Herein, we use Monte Carlo simulation to study the coil-to-globule transition of simple compact polymer chains. We first consider the finite-size effects for a given monomer interaction, where the short chain exhibits a one-step collapse while long chains demonstrate a two-step collapse, indicated by the specific heat. More interestingly, with the decrease of chain monomer interaction, the critical temperatures marked by the peaks of heat capacity shift to low values. A closer examination from the energy, mean-squared radius of gyration and shape factor also suggests the lower temperature of coil-to-globule transition.